Continuous‐Time Autoregressive Moving Average Processes in Discrete Time: Representation and Embeddability

10 Pages Posted: 24 Aug 2013

See all articles by Michael A. Thornton

Michael A. Thornton

University of York

Marcus J. Chambers

University of Essex - Department of Economics

Date Written: September 2013

Abstract

This article explores techniques to derive the exact discrete‐time representation for data generated by a continuous‐time autoregressive moving average (ARMA) process, augmenting existing methods with a stochastic integration‐by‐parts formula. The continuous‐time ARMA(2, 1) system is considered in detail, and a mapping from the parameters of a univariate discrete‐time ARMA(2, 1) process to a univariate continuous‐time ARMA(2, 1) process observed at discrete intervals is derived. This is used to derive conditions for the embeddability of such processes.

Keywords: Continuous time, ARMA process, discrete‐time representation, embedding

Suggested Citation

Thornton, Michael A. and Chambers, Marcus J., Continuous‐Time Autoregressive Moving Average Processes in Discrete Time: Representation and Embeddability (September 2013). Journal of Time Series Analysis, Vol. 34, Issue 5, pp. 552-561, 2013. Available at SSRN: https://ssrn.com/abstract=2315414 or http://dx.doi.org/10.1111/jtsa.12030

Michael A. Thornton (Contact Author)

University of York ( email )

Heslington
University of York
York, YO10 5DD
United Kingdom

Marcus J. Chambers

University of Essex - Department of Economics ( email )

Wivenhoe Park
Colchester CO4 3SQ
United Kingdom

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